The document summarizes an optimization technique used to adjust air pollution emissions rates in an air quality model using data from low-cost air quality sensors. The technique develops an inversion method to automatically adjust emissions inputs to improve model predictions against monitored concentrations. Preliminary tests of the technique in Cambridge, UK optimized NOx emissions rates from 305 road sources against data from 20 low-cost sensors and 5 reference monitors. The optimization reduced errors between modeled and monitored concentrations and adjusted emissions profiles and rates in a physically reasonable manner.

1. Amy Stidworthy
DMUG
6h April 2017
London
Optimising local air quality models
with sensor data: examples from
Cambridge

2. DMUG, London, 6th April 2017
Acknowledgements
• The work presented here has been done by CERC based on
ADMS-Urban modelling of Cambridge following the
deployment of AQMesh sensors in Cambridge. Partners
include:
– Rod Jones & Lekan Popoola, Department of Chemistry, University
of Cambridge
– Dan Clarke, Cambridgeshire County Council, Cambridge
– Jo Dicks & Anita Lewis, Cambridge City Council, Cambridge
– Ian Leslie, Computer Laboratory, University of Cambridge
– Amanda Randle, AQMesh

3. DMUG, London, 6th April 2017
Outline of presentation
• Motivation
• Optimisation technique
• Preliminary results for Cambridge
• Further work

4. DMUG, London, 6th April 2017
Motivation
• Emissions errors account for a significant proportion of
dispersion model error
• Traditionally, dispersion models such as CERC’s ADMS-Urban
model are validated against data from reference monitors:
– Modellers either use the validation to improve model setup; or
– Calculate and apply a model adjustment factor to model results
• New low cost air pollution sensors allow large networks of
sensors to be installed across a city
• Accuracy and reliability is generally lower than reference
monitors, but larger spatial coverage is possible
• How can we best use these sensor data in modelling?
• If the data are not accurate and reliable enough for model
validation, maybe we can use the data in a different way...

5. DMUG, London, 6th April 2017
Optimisation technique: Overview
• The aim is to develop an inversion technique to use monitoring
data from a network of sensors to automatically adjust
emissions to improve model predictions
• Basic idea:
– Run ADMS-Urban to obtain modelled concentrations at monitor
locations in the normal way
– Use these modelled concentrations and their associated
emissions as a ‘first guess’, together with
a) monitored concentration data
b) information about the error in the monitored data and the proportion
of that error that is systematic across all monitors
c) Information about the error in the emissions data and the proportion
of that error that is systematic across all sources
– Use an inversion technique to calculated an adjusted set of
emissions that reduces error in the modelled concentrations

6. DMUG, London, 6th April 2017
Optimisation technique: Introduction
• There are some conditions that have to be satisfied for such a
scheme to work:
a) The model concentration must be proportional to the emissions,
which means that complex effects like chemistry have to be
ignored
b) Any sources included must affect at least one receptor (monitor)
c) Any receptor included must have non-zero concentration
• The technique developed uses a probabilistic approach
following work by others, for example as used by the Met
Office for estimating volcanic ash source parameters using
satellite retrievals [Webster et al, 2016]

7. DMUG, London, 6th April 2017
Optimisation technique: Cost function
We define a cost function J(x) with two terms: one that describes
the error in the modelled concentration (left-hand term) and one
that describes the error in the emissions (right-hand term)
The aim is to minimise J to obtain x, a vector of adjusted
emissions.
Quantity Definition Dimensions
x Vector of emissions (result) n
M Transport matrix relating the source term to the observations n by k
y Vector of observations k
R Error covariance matrix for the observations k by k
e Vector of first guess emissions n
B Error covariance matrix for the first guess emissions n by n
         exBexyMxRyMxx   11 TT
J

8. DMUG, London, 6th April 2017
Optimisation technique: Least squares problem
• To solve the cost function minimisation problem, we first convert
the problem to a ‘least squares’ problem, which is easier to solve
computationally
• A ‘least squares’ problem finds the best solution to the equation
Ax=f, where x is a vector of size m, f is a vector of size n and A is
a matrix with n rows and m columns.
• The result of solving the least squares problem is the vector x
that gives the minimum value of the sum of the squares of the
elements of (Ax-f)
• So, we need to write the cost function as
Fast forward through the maths...
     fAxfAx 
T
xJ

9. DMUG, London, 6th April 2017
Optimisation technique: Error covariance matrices
• To solve the problem, we need to construct the matrix A and the vector
f, but do we have all the information we need for this?
 M is the transport matrix: this represents the contribution of every
source to every receptor given a unit emission rate
 y is the vector of monitored concentrations at each receptor
 e is the vector of emissions for each source
• What are the matrices T and D?
 These are the related to the ‘covariance’ matrices R and B that
represent the error in the monitored data and emissions data
respectively.
 The diagonal components of the covariance matrices represent the
variance in the data, which is related to the uncertainty in the data;
 The off-diagonal components represent how much of the error is ‘co-
varying’, or in other words, systematic.
      











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



eD
yT
f
D
MT
AfAxfAx T
T
T
T
T
xJ and

10. DMUG, London, 6th April 2017
Optimisation technique: Monitoring data error
• The diagonal components of the monitoring data error
covariance matrix R represent the variance σObs
2 of the
monitored data, which is the square of the standard deviation
σObs:
– We assume that the standard deviation σObs is equal to the
uncertainty in the monitoring data expressed as a concentration
and is equal to Uobs x O, where Uobs is the uncertainty expressed
as a fraction.
• The off-diagonal components represent the error that co-varies
between monitors, i.e. systematic error
– We say that a given proportion of the uncertainty is due to
systematic error

11. DMUG, London, 6th April 2017
Optimisation technique: Monitoring data error
• So, for any two monitors labelled i and j, their covariance is
defined as
• The factor UfObs represents the fraction of the monitoring data
uncertainty that is due to systematic error.
• This raises questions:
– How much of monitoring data error is systematic?
– Should monitors of different types be treated as independent, with
no co-variance?
– Are there any causes of monitoring data error that affect all
monitors, e.g. temperature, humidity?
– Is there co-variance between sensors for different pollutants?
     
     





jijyUUfiyUUf
jiiyU
ji
ObsObsObsObs
Obs
Obs
2
2
,

12. DMUG, London, 6th April 2017
Optimisation technique: Emissions data error
• The diagonal components of the emissions error covariance
matrix B represent the variance σEm
2 of the emissions data,
which is the square of the standard deviation σEm:
– We assume that the standard deviation σEm is equal to the
uncertainty in the emissions data expressed as a concentration
and is equal to Uem x E, where Uem is the uncertainty expressed
as a percentage.
• The off-diagonal components represent the error that co-varies
between sources, i.e. systematic error
– We say that a given proportion of the uncertainty is due to
systematic error, for example traffic emissions factors

13. DMUG, London, 6th April 2017
Optimisation technique: Emissions data error
• So, for any two sources labelled i and j, their covariance is
defined as
• The factor UfEm represents the fraction of the emissions data
uncertainty that is due to systematic error.
• This also raises questions:
– How much of the emissions data error is systematic? For
example, what proportion of road emissions data is due to errors
in the emission factors (systematic) and how much is due to traffic
counts (non-systematic)
– Is there any co-variance in the emissions data error for different
pollutants? PM10 and PM2.5 – yes, but PM10 and NOX?
     
     
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
jijeUUfieUUf
jiieU
ji
EmEmEmEm
Em
Em
2
2
,

14. DMUG, London, 6th April 2017
Preliminary results: Cambridge
• CERC have been collaborating on a project to study
ambient air quality across Cambridge using a large
number of sensor nodes and computer modelling.
• 20 AQMesh sensor pods have been placed at key
points around Cambridge, measuring air quality in near
real time.

15. DMUG, London, 6th April 2017
Preliminary results: Cambridge
• The aim of the preliminary Cambridge tests presented here is
primarily to examine the behaviour of the optimisation scheme
and refine the process, i.e.
– Does it work?!
– Is it practical? If it takes weeks to run then obviously not.
– What effect does the choice of uncertainty parameters have on
outcome?
– How does the validation at the reference monitors change?
– Can we learn anything about emissions?

16. DMUG, London, 6th April 2017
ADMS-Urban model setup
• One source type: 305 road sources
• One pollutant: NOX
• 25 monitors: 20 AQMesh monitors and 5 reference monitors
• Time-varying emission factors: diurnal profiles for weekdays,
Saturdays and Sundays
• Daylight saving option used to obtain correct emission factors
• 3-month period: 30/06/2016 01:00 to 30/09/2016 23:00

17. DMUG, London, 6th April 2017
Optimisation process
Step 1: Run ADMS-Urban to obtain modelled
concentrations at monitoring site locations
Step 2: Form the transport matrix, emissions
vector and monitored data vector
Step 3: Run the optimisation scheme
Step 4: Create an hourly factors (.hfc) file
from the adjusted emissions data
Step 5: Re-run ADMS-Urban using the
adjusted emissions .hfc file

18. DMUG, London, 6th April 2017
Optimisation parameters
• As described previously, we specify the following parameters
in the optimisation:
EU
Parameter name Description
Uobs(ref) Observation uncertainty (reference monitors)
Uobs(aqmesh) Observation uncertainty (AQmesh sensors)
Ufobs(ref) Observation uncertainty covariance factor
(reference monitors)
Ufobs(aqmesh) Observation uncertainty covariance factor
(AQmesh sensors)
Uem Emissions uncertainty
Ufem Emissions uncertainty covariance factor

19. DMUG, London, 6th April 2017
Optimisation Technique: Effect of uncertainty
Optimisation is working!
J is reduced for all uncertainty
values
Increasing Ou relaxes the
constraints so J is reduced less

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AQMesh sensors: more model error toleratedRef: less model
error tolerated
0
50
100
150
200
250
300
NOxconcentration(ug/m3)
Observed Model (original emissions) Model (adjusted emissions, all sensor data)
Effect of monitor uncertainty on concentrations
• In these inversion calculations:
– Reference monitor uncertainty set to 10%
– AQMesh sensor uncertainty set to 30%
– Covariance between Reference monitors (systematic error) set to 5%
– Covariance between AQMesh sensors (systematic error) set to 10%
– No covariance between Reference monitors and AQMesh sensors
Example hour: 7am on 5th July

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Effect of emissions covariance on adjusted emissions
-100%
-50%
0%
50%
100%
150%
200%
Percentage increase in source emission rate with different emissions
error covariance settings
Zero emissions error covariance
75% emissions error covariance
• If emissions error covariance is zero, emissions can
change completely independently
• With non-zero emissions error covariance, emissions
have to change more consistently across all sources

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Cambridge: optimisation parameters used
Parameter
name
Description Value
Uobs(ref) Observation uncertainty (reference monitors) 0.1
Uobs(aqmesh) Observation uncertainty (AQmesh sensors) 0.3
Ufobs(ref) Observation uncertainty covariance factor
(reference monitors)
0.05
Ufobs(aqmesh) Observation uncertainty covariance factor
(AQmesh sensors)
0.1
Uem Emissions uncertainty 0.5
Ufem Emissions uncertainty covariance factor 0.4
All monitoring data are provisional apart from Gonville Place
reference monitor; AQMesh data were obtained in real time.

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Effect of optimisation on model validation
Statistics 1. 2. 3.
Mean
Obs 31.2 31.2 31.2
Mod 34.5 29.3 31.3
StDev
Obs 27.9 27.9 27.9
Mod 31.0 26.0 27.0
MB 3.30 -1.91 0.10
NMSE 0.51 0.05 0.39
R 0.70 0.97 0.75
Fac2 0.71 0.94 0.73
1. Orig_RdsOnly
Base case model output
2. Inv_ReRun_AllSensors
Model output using optimised emissions;
optimisation carried out using all sensor data
3. Inv_ReRun_AQMeshSensorsOnly
Model output using optimised emissions;
optimisation carried out using AQMesh data
only
Validation at
Reference
sites only
Data points not
included in the
inversion

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Effect of optimisation on diurnal emissions profiles
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22
Weekday Saturday Sunday
Emissionfactor
Diurnal emission factor profiles: original and adjusted emissions
Original
Adjusted, all sensors
Adjusted, AQMesh sensors only

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Effect of optimisation on mean emission rates
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Meanadjustedemissionrate(g/km/s)
Mean first-guess emission rate
Optimisation using AQMesh
sensor data only
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Meanadjustedemissionrate(g/km/s)
Mean first-guess emission rate
Optimisation using AQMesh
sensor data and reference
monitor data

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Effect of optimisation on mean emission rates
Average % change
-2.8%
-60.0%
-40.0%
-20.0%
0.0%
20.0%
40.0%
60.0%
Optimisation using AQMesh sensor data only
Percentage change in mean emission rate per road source
Average % change
-3.0%
-60.0%
-40.0%
-20.0%
0.0%
20.0%
40.0%
60.0%
Optimisation using AQMesh sensor data and reference monitor data
Including reference data causes
big changes in just a few sources

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Example output at reference monitors: 5th July 2016
Montague Rd
Regent St
Gonville Place
Parker St
Newmarket Rd

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7-day average concentration: Adjusted - Original
Example of how the
optimisation process
affects
concentration
contours:
General reduction,
but increase in
some areas
+30
-30
NOX ug/m3
0

29. DMUG, London, 6th April 2017
Discussion and further work
• We have developed an optimisation scheme to use data from a
network of sensors to automatically adjust emissions and thereby
improve model results
• Tests show that the scheme works and initial results are
encouraging, but there is more work to do, for example:
– More than 1 pollutant
– Other source types
• The optimisation scheme run times are also encouraging: approx 15
minutes to run 3 months of hourly data with 305 sources and 25
receptors, carrying out the optimisation for each individual hour
• The values of uncertainty and covariance factors used so far are
largely arbitrary; we need to use realistic values to obtain meaningful
results
• After Cambridge, the next step is to run the scheme with sensor data
collected at Heathrow during the NERC SNAQ project.

30. DMUG, London, 6th April 2017
Thank you
• Thanks again to CERC’s partners in this work:
– Rod Jones & Lekan Popoola, Department of Chemistry, University
of Cambridge
– Dan Clarke, Cambridgeshire County Council, Cambridge
– Jo Dicks & Anita Lewis, Cambridge City Council, Cambridge
– Ian Leslie, Computer Laboratory, University of Cambridge
– Amanda Randle, AQMesh
• For more information about the ADMS-Urban dispersion
model, see www.cerc.co.uk/Urban